Joined Common Chords of Napoleon's Circumcircles
What is this about?
An Equilateral Triangle in Napoleon's Circumcircles
Let $ABC',$ $BCA',$ and $CAB'$ be Napoleon's triangles constructed on the sides of $\Delta ABC.$ Choose point $D$ on the circumcircle $ABC',$ pass it through $A$ to the intersection $F$ with $C(CAB')$ and through $E$ to the intersection $E$ with $C(BCA').$
Triangles $DEF$ is equilateral.
The problem is very simple; it submits to chasing inscribed angles.
The solution is outlined in an old variant of this problem.
The problem described on this page stems from an observation of Hirotaka Ebisui.